Parafree metabelian Lie algebras which are determined by parafree Lie algebras

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

Let L be a Lie algebra. Denote by δ^{k}(L) the k-th term of the derived series of L and by Δ_{w}(L) the intersection of the ideals I of L such that L/I is nilpotent. We prove that if P is a parafree Lie algebra, then the algebra Q=(P/δ^{k}(P))/Δ_{w}(P/δ^{k}(P)), k≥2 is a parafree solvable Lie algebra. Moreover we show that if Q is not free metabelian, then P is not free solvable for k=2.

Keywords:

Parafree Lie algebras, metabelian Lie algebras solvable Lie algebras,

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Baumslag, G., Groups with the same lower central sequence as a relatively free group I. The groups, Trans. Amer. Math. Soc., 129(1967), 308-321.
Baumslag, G., Groups with the same lower central sequence as a relatively free group. II Properties, Trans. Amer. Math. Soc., 142(1969), 507-538.
Baumslag, G., Parafree groups, Progress in Math., 248(2005), 1-14.
Baumslag, G., and Cleary, S., Parafree one-relator groups, J. Group Theory, 9(2006), 191-201.
Baumslag, G., and Cleary, S. And Havas, G., Experimenting with infinite group, Experimental Math., 13(2004), 495-502.
Baur, H., Parafreie Liealgebren und homologie, Diss. Eth Nr. 6126, (1978), 60 pp.
Baur, H., A note on parafree Lie algebras, Commun. in Alg., 8(1980), No.10 953-960.
Ekici, N. and Velioğlu, Z., Unions of Parafree Lie Algebras, Algebra, 2014(2014), Article ID 385397.
Ekici, N. and Velioğlu, Z., Direct Limit of Parafree Lie Algebras, Journal of Lie Theory 25(2015), No. 2 477-484.